A Catalog of Narrow Line Seyfert 1 Galaxies from the Sloan Digital Sky Survey Data Release 12

The spectra of low-redshift AGNs may contain a significant contribution from the host galaxy starlight. To elucidate important information on AGN properties from the spectra, the stellar light contribution needs to be removed. We used the simple stellar population (SSP) method to remove the contribution of host galaxy from the spectra and estimated the stellar properties following Zhang (2014) and Zhang & Feng (2016). The observed spectrum, $F(\lambda )$, can be modeled using SSP method as follows:

$$\begin{eqnarray}&&F(\lambda )=\left[\displaystyle \sum _{i=1}^{39}{a}_{i}\times {F}_{\mathrm{ssp}}(\delta \lambda ,{r}_{\lambda })\right]\ast g(\lambda ,{\sigma }_{* })+{F}_{\mathrm{AGN}}(\lambda ,{r}_{\lambda }),\end{eqnarray} \tag{ 1 }$$

where the first part of the right-hand side represents the contribution of host galaxy starlight and the second part represents the AGN contribution. Here a_i is the amplitude of the individual SSP templates, ${F}_{\mathrm{ssp}}(\delta \lambda ,{r}_{\lambda })$ is the SSP template with a wavelength shift of $\delta \lambda$ and reddening factor of ${r}_{\lambda }$, $g(\lambda ,{\sigma }_{* })$ is the Gaussian broadening function with velocity ${\sigma }_{* }$ considered as the stellar velocity dispersion, and ${F}_{\mathrm{AGN}}(\lambda ,{r}_{\lambda })$ is the contribution from the AGN in the form of ${\lambda }^{\alpha }$ with the reddening correction factor ${r}_{\lambda }$ (α is the power-law index). The summation runs from i = 1 to 39 as the SSP model is applied with 39 simple stellar template spectra. The templates were taken from Bruzual & Charlot (2003) having ages between 5 Myr and 12 Gyr and solar metallicities of Z = 0.008, 0.05, and 0.02. A detailed description of the SSP method is given in Bruzual & Charlot (2003), Kauffmann et al. (2003), Wang et al. (2009), Cappellari et al. (2012), and Zhang (2014).

We masked the emission lines without considering the Fe ii multiplets as emission lines so as to leave sufficient continuum windows for continuum fitting and performed Levenberg–Marquardt least-squares minimization using IDL mpfit⁵ fitting package (Markwardt 2009) to fit the spectra. This allowed us to decompose the contribution of the host galaxy and AGN continuum from the spectra. We then subtracted the contribution of the host galaxy stellar light from the spectra without subtracting AGN global continuum. Figure 1 shows examples of starlight subtraction from the spectra. The decomposed AGN continuum emission component is shown by a solid green line, host galaxy contribution is shown by a solid blue line. We note that the continuum fitting procedure is phenomenological, which is sufficient for the present study.

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After subtracting the starlight contribution from the spectra as described above, we performed a simultaneous fitting of emission lines including one local power-law continuum component around Hβ and Hα regions along with recent high-quality Fe ii template spectra taken from Kovačević et al. (2010). In the Hβ region, with a wavelength range of 4385–5500 Å, apart from Hβ (having both narrow and broad components) the lines fitted are He iiλ4687 Å and [O iii]λ 4959, 5007 Å doublet (with two Gaussian functions). In the Hα region, with a wavelength range 6280–6750 Å, the lines used in the fitting process are the narrow [O i]λ6300, 6363 Å, narrow [N ii]λ6548, 6583 Å doublet, and the narrow [S ii]λ6716, 6731 Å doublet along with Hα. Each of the narrow components are fitted with a single Gaussian having a maximum FWHM of 1200 km s⁻¹, following Shen et al. (2011). From theoretical arguments, Goad et al. (2012) suggest that the Balmer lines of NLSy1 galaxies are expected to have Lorentzian profile caused by the microscopic turbulence velocity of BLR clouds enhancing the line wings relative to the core, especially at a large radius. Observationally, it has also been noticed that the observed broad Balmer lines are best characterized by a Lorentzian than a Gaussian profile (Moran et al. 1996; Véron-Cetty et al. 2001; Sulentic et al. 2002; Cracco et al. 2016).

In our fitting process, when both Hβ and Hα regions are fitted simultaneously, we allow a single Gaussian and Lorentzian functions for fitting both the broad Balmer components, where the algorithm automatically chooses among these functions the best-fitted function, which gives a similar width for both broad components of Balmer lines, Hβ and Hα. We also find that, in our fitting, the Lorentzian function is preferred compared to the Gaussian function, confirming the earlier claims by various authors as discussed above. This led us to choose a single Lorentzian function to model the broad component of Hβ when only the Hβ region was fitted. Note that if the narrow Hβ/Hα component is not required with the broad component, our iterative fitting procedure automatically drops it during minimization.

Spectral coverage of SDSS and BOSS allows us to carry out a simultaneous fitting of both Hα and Hβ regions for $z\lt 0.3629$, and for higher z (up to 0.8) only fitting of Hβ region was performed. During the fitting, the flux ratios of [O iii] and [N ii] doublets were fixed to their theoretical values, i.e., $F(5007)/F(4959)=3$ and $F(6585)/F(6549)=3$. Widths of all the narrow components in the Hβ region were tied with the narrow [O iii] line width and the redshift of each doublet was tied together (see Shen et al. 2011). Similarly, in the Hα region, widths of all the narrow components were tied together with narrow [N ii]λ6583 Å. A final fitting was carried out by simultaneously varying all the free parameters using Levenberg–Marquardt least-squares minimization, allowing us to estimate all emission line parameters including Fe ii parameters along with the nuclear continuum contribution. Figure 2 shows few examples of emission line fitting around Hβ (left) and Hα (right). The corresponding residual plots are shown in the lower panels.

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Using the fitting procedure outlined above, we have arrived at a new sample of NLSy1 galaxies. For a consistency check, it will also be useful to test whether in our procedure we are able to retrieve the sample of NLSy1 galaxies reported by ZH06 using SDSS DR3. For that, we compared our sample with that of ZH06. We found that 1815 out of the 2011 sources reported by ZH06 are included in our sample. Our fitting procedure is thus able to recover 90% of the sources found by ZH06. The 10% of sources that are in the ZH06 sample but missed in our catalog might be due to (1) the fact that our selection considered the width of Hβ ≤ 2200 km s⁻¹, whereas ZH06 considered either of the two Balmer lines⁷ to have FWHM ≤ 2200 km s⁻¹ and (2) that the ZH06 sample has 29 NLSy1 classified as "galaxy" in SDSS DR3, which are not included in our parent catalog of 114,806 candidates as our selection only considers the sources classified as "QSO" by SDSS pipeline. For those sources that are common to ours and the ZH06 sample, we found that typical errors in the FWHM of the Hβ broad component are around 5%, which is similar to the value of 6% quoted by ZH06. However, considering our whole sample of 11,101 sources, the median error in the FWHM of the Hβ broad component is around 7%.

In Figure 5, we compare our measurements with the values obtained by ZH06 for all the objects that are included in both of the catalogs. The nuclear monochromatic luminosity⁸ (upper left), broad Hβ line flux (upper middle), broad Hβ FWHM (upper right), flux of [O iii]λ 5007 Å (lower left), flux of Fe ii (4434–4684 Å; lower middle), and strength of Fe ii i.e., R₄₅₇₀ (lower right), defined as the ratio of Fe ii flux in the wavelength range 4434 Å–4684 Å to the Hβ broad component flux, are shown in the plot. The circles represent objects having $z\gt 0.3629$, i.e., for the objects in which only the Hβ region is fitted while the empty squares are objects having $z\lt 0.3629$ in which both Hβ and Hα regions are fitted simultaneously. Our estimated $\lambda {L}_{\lambda }(5100\,{\mathring{\rm{A}}} )$ closely matches with the measurements of ZH06. The logarithmic ratio of these two measurements has an average of 0.02 ± 0.17. Similarly, close matches between measurements of Hβ and [O iii] line flux have also been found with the logarithmic ratio distribution having an average of −0.04 ± 0.08 and −0.02 ± 0.10 respectively. The Fe ii flux and its strength are found to be similar to those of ZH06. The logarithmic ratio between our measurements to that of ZH06 has an average of −0.07 ± 0.19 and −0.03 ± 0.17 for Fe ii flux and R₄₅₇₀ respectively. The close correspondence between various physical quantities (shown in Figure 5) deduced from the fitting process outlined here with those reported by ZH06 for sources that are common to the two studies, indicates the robustness of the fitting procedure adopted in this work.

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The width of the Hβ broad emission line we measured also closely matches the measurement of ZH06. The ratio of these two measurements has a mean of 1.08 with a dispersion of 0.22. From the figure, it is evident that the Hβ widths of some objects having $z\lt 0.3629$, represented by empty square symbols, are overestimated in this work compare to ZH06 and deviate from the unit ratio line in some cases. This might be due to the differences in the fitting procedure adopted in this work and that used by ZH06. This overestimation of the FWHM of Hβ broad component for some objects by us could lead to some genuine NLSy1 galaxies being missed out, however, it would definitely prevent non-NLSy1 galaxies from being included in the sample. Also, our ability to retrieve 90% of the sources found by ZH06 reiterates the fact that our fitting procedure is robust, despite the minor difference in the methodology adopted in this work and that used in ZH06.

The number of SDSS sources identified as "QSO" by the SDSS pipeline with z < 0.8 and a median ${\rm{S}}/{\rm{N}}\gt 2\,{\mathrm{pixel}}^{-1}$ in SDSS DR12 is 68,859. From this initial set of sources, the number of NLSy1 galaxies selected based on our criteria is 11,101, which is about 16% of our original sample of broad-line AGNs. This is consistent with what is found earlier by Osterbrock (1988), Véron-Cetty et al. (2001), and ZH06. The redshift distribution and absolute g-band magnitude of all the BLAGN (parent sample: empty-hatched) and NLSy1 galaxy sample (filled region) are shown in Figure 6. The number of BLAGN increases with redshift in our parent sample, though the NLSy1 galaxies seem to be equally populated throughout $z\lt 0.8$. On the other hand, the absolute g-band magnitude distribution of both BLAGN and NLSy1 galaxies peaks at ${M}_{g}\sim -22$ mag. A similar peak in the absolute magnitude distribution is also noted by ZH06.

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Greene & Ho (2005) found a strong correlation between the luminosity of Balmer lines and optical continuum luminosity. Interestingly, such relations are valid over a wide range of luminosity (${10}^{42}\lt {L}_{5100}\lt {10}^{47}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$) and redshift ($0\lt z\lt 6$), suggesting that the response of the BLR to the incident continuum is consistent across all redshifts and luminosities, i.e., the physical mechanism governing the correlation is the same in all AGNs (Jun et al. 2015). We estimated the luminosity of Hβ and Hα for all the objects in our sample having $0\lt z\lt 0.8$ and $0\lt z\lt 0.3629$ respectively. The correlation of monochromatic luminosity at 5100 Å with the luminosity of Hβ (top), Hα (middle), and [O iii]λ5007 Å (bottom) is shown in Figure 7. All correlations are very strong, as found earlier by various authors (e.g., Greene & Ho 2005; Zhou et al. 2006; Jun et al. 2015). Linear least-squares fit yields

$$\begin{eqnarray}\mathrm{log}({L}_{{\rm{H}}\beta }) & = & (-5.53\pm 0.21)+(1.084\pm 0.004)\\ & & \times \mathrm{log}(\lambda {L}_{\lambda }(5100\,{\mathring{\rm{A}}} )).\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}\mathrm{log}({L}_{{\rm{H}}\alpha }) & = & (-0.17\pm 0.34)+(0.971\pm 0.007)\\ & & \times \mathrm{log}(\lambda {L}_{\lambda }(5100\,{\mathring{\rm{A}}} )).\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}\mathrm{log}({L}_{[{\rm{O}}{\rm{III}}]}) & = & (9.87\pm 0.29)+(0.721\pm 0.006)\\ & & \times \mathrm{log}(\lambda {L}_{\lambda }(5100\,{\mathring{\rm{A}}} )).\end{eqnarray} \tag{ 4 }$$

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The dashed line in the middle panel of Figure 7 represents the relation found by Jun et al. (2015), where they studied an ${L}_{{\rm{H}}\alpha }\mbox{--}{L}_{5100}$ relationship over a wide range of luminosity and redshift ($0\lt z\lt 6$). The strong correlations between Balmer line luminosity and continuum luminosity over a wide range of luminosity and redshift suggest that the former can be used in measuring black hole mass when the latter is subjected to large uncertainty, especially in some AGNs, where the host galaxy contamination or emission from the jet is significant and optical continuum luminosity is difficult to estimate (e.g., Greene & Ho 2005). The relation of [O iii] luminosity and continuum luminosity is particularly useful to measure intrinsic luminosity and the black hole mass of narrow emission line AGNs based on [O iii] luminosity (e.g., Zakamska et al. 2003).

One of the main characteristics of NLSy1 galaxies is that they have strong Fe ii emission (Vanden Berk et al. 2001; Zhou et al. 2006). The value of Fe ii strength (R₄₅₇₀) in a typical AGN is ∼0.4 (see, Bergeron & Kunth 1984 and the reference therein) and about 0.8 in NLSy1 galaxies, as reported by ZH06. Our original sample provides us with a list of BLSy1 galaxies (${\mathrm{FWHM}}_{{\rm{H}}\beta }\gt 2200\,\mathrm{km}\,{{\rm{s}}}^{-1}$), allowing us to compare the Fe ii strengths between NLSy1 and BLSy1 galaxies. The distributions of R₄₅₇₀ for both the samples are shown in Figure 8. The distribution for NLSy1 galaxies (solid line) peaks at larger R₄₅₇₀ having a mean and 1σ dispersion of 0.64 and 0.40, respectively, compared to the BLSy1 galaxies (dashed line), which has a mean and 1σ dispersion of 0.38 and 0.34, respectively. The Kolmogorov–Smirnov (K-S) two-sample test rejects the null hypothesis with a p-value of $\lt 1\times {10}^{-100}$ that the two distributions are drawn from the same population. This is consistent with the earlier results in the literature (e.g., see, Vanden Berk et al. 2001; Zhou et al. 2006) and clearly indicates that NLSy1 galaxies are stronger Fe ii emitters than BLSy1 galaxies. In our sample about 60% NLSy1 galaxies have ${R}_{4570}\gt 0.5$, about 16% show moderately strong Fe ii emission with ${R}_{4570}\gt 1$, and about 0.5% show super strong Fe ii emission (${R}_{4570}\gt 2.0;$ Lawrence et al. 1988). According to Gaskell (1985), the reason for having large R₄₅₇₀ in NLSy1 galaxies is due to their weak Hβ line instead of their strong Fe ii emission.

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In Figure 9, we plotted Fe ii strength against the FWHM of broad Hβ (left) and Hα (right) of our sample. It is clear that there is a weak anti-correlation with the Spearman correlation coefficient of −0.18 in both cases (with a p-value of $1\times {10}^{-21}$ and $1\times {10}^{-29}$ respectively). This weak correlation in NLSy1 galaxies is consistent with the correlation found by ZH06. In Figure 10, we show the correlation between different derived parameters of our NLSy1 galaxy sample. No correlation is found between Hβ luminosity and R₄₅₇₀ (top left). We also calculated the equivalent widths (W) of Fe ii and Hβ lines by the ratio of line flux to the continuum flux at 5100 Å i.e., $W={F}_{\mathrm{line}}/{F}_{c}(\lambda =5100\,{\mathring{\rm{A}}} )$. Interestingly, both W(Fe ii) and W(Hβ) are found to be strongly correlated with the luminosity of Hβ line and monochromatic luminosity at 5100 Å (second and third panels). This is indeed similar to what was found by ZH06 and partially in agreement with Véron-Cetty et al. (2001) who found that the Hβ luminosity is not correlated with the equivalent width of Fe ii but correlated with Hβ. The presence of such strong correlations suggest that NLSy1 galaxies are indeed a different class of objects compared to BLSy1 galaxies because the latter generally show no or very weak correlation. Moreover, a strong correlation between ${R}_{4570}$ and W(Fe ii) (r = 0.5), and an anti-correlation between ${R}_{4570}$ with the equivalent width of Hβ has been found (fourth panel). This suggests that the observed large ${R}_{4570}$ is not only due to weak Hβ but also due to strong Fe ii, which is in agreement with Cracco et al. (2016) and partially in disagreement with Gaskell (1985). Also shown in Figure 10 is the correlation between Hβ luminosity against R₅₀₀₇, which is the ratio of total [O iii] flux to total Hβ (broad+narrow) flux (${R}_{5007}=f{[{\rm{O}}{\rm{III}}]}^{\mathrm{tot}}/f{({\rm{H}}\beta )}^{\mathrm{tot}}$; the top-right corner). An anti-correlation is found that could be related to the weakness of Hβ in low-luminosity objects (middle-left panel) as found in Vanden Berk et al. (2001).

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Objects with strong Fe ii emission are found to have weak [O iii] lines and vice versa (Grupe et al. 1999; McIntosh et al. 1999; Barrows et al. 2012); however, evidence of such anti-correlation has not been noted by Véron-Cetty et al. (2001). Several correlations of our NLSy1 galaxies are plotted in Figure 11. We find a weak anti-correlation between R₅₀₀₇ and R₄₅₇₀ (first panel, $r=-0.22$), a strong anti-correlation between R₅₀₀₇ and W(Fe ii) (second panel, $r=-0.59$), a weak anti-correlation between W([O iii]) and W(Fe ii) (third panel, $r=-0.20$), and a moderately strong anti-correlation between W([O iii]) and R₄₅₇₀ (fourth panel, $r=-0.47$). These observations thus confirm that Fe ii strength is indeed stronger when [O iii] is weak in NLSy1 galaxies.

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NLSy1 galaxies are generally radio quiet⁹ with the radio loudness parameter $R\lt 10$. A fraction of about 7% of their population are known to be radio loud with $R\gt 10$, and a very small fraction of about 2.5% are found to be very radio loud with $R\gt 100$ (Komossa et al. 2006). The fraction of radio-loud NLSy1 galaxies is indeed small compared to the 15% we know in the quasar category of AGNs (Kellermann et al. 1989). However, the radio-loud quasar fraction is found to depend on redshift and luminosity and this fraction could be larger than 20% in low-redshift AGNs (Jiang et al. 2007). It is important to find more radio-loud NLSy1 galaxies, due to the discovery of γ-ray emission in half-a-dozen of them by Fermi, which argues for the presence of relativistic jets in these sources (e.g., see, Paliya et al. 2015). With an aim to find more radio-loud NLSy1 galaxies, we cross-correlated our sample with the FIRST survey (Catalog version 14dec17¹⁰ ) within a search radius of 2''. We find that about 555 sources (5%) are detected by FIRST.

In Figure 12, we show the distribution of logarithmic radio loudness (we define radio loudness as the ratio of 1.4 GHz flux to optical g-band flux, $R={F}_{1.4\mathrm{GHz}}/{F}_{{\rm{g}}}$) in the upper panel, the distribution of radio power (middle panel), and the correlation between radio power and luminosity of [O iii] (lower panel). The radio power (${P}_{1.4}$) was estimated using ${P}_{1.4}=4\pi {D}_{L}^{2}{(1+z)}^{(\beta -1)}{\nu }_{0}{F}_{{\nu }_{0}}$ (Cavagnolo et al. 2010), where ${\nu }_{0}$ is the observed frequency of 1.4 GHz, D_L is the luminosity distance, and β is the radio spectral index taken to be 0.8 (Condon 1992). The $\mathrm{log}R$ distribution has a mean of 1.49 ± 0.82. Out of the 555 NLSy1 galaxies that are detected by FIRST, 177 are radio quiet ($R\lt 10$) and 378 are radio loud ($R\gt 10$). Their radio power ranges between log ${P}_{1.4}=37.6$ to $43.3\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ having a peak at about $40.5\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. The distribution of $\mathrm{log}{P}_{1.4}$ has a mean of $40.0\pm 1.0\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, which is similar to the mean value of $\mathrm{log}{P}_{1.4}$ of $40.6\pm 1.1\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ found for the radio-detected BLSy1 galaxies in our sample indicating the influence of possible selection effects present in our sample of radio-detected sources. The 1.4 GHz radio power (${P}_{1.4}$) is found to be correlated with the luminosity of [O iii]. The Spearman correlation coefficient r = 0.52 with a p-value $1\times {10}^{-41}$ confirms a strong positive correlation between these two parameters. A linear fit (solid line) yields

$$\begin{eqnarray}&&\mathrm{log}({P}_{1.4})=(0.976\pm 0.06)\times \mathrm{log}({L}_{[{\rm{O}}{\rm{III}}]})-(0.73\pm 2.78).\end{eqnarray} \tag{ 5 }$$

This is similar to the correlation between radio power at 6 cm and luminosity of [O iii] found by Greene & Ho (2007) for low-mass AGNs. However, dividing our radio-detected NLSy1 galaxies into different redshift ranges with bin size of 0.2, we found the correlation to vanish in all redshift bins except for $z\lt 0.2$.

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NLSy1 galaxies are known to show steep soft X-ray spectra and rapid X-ray variability. To find the X-ray counterparts to our sample, we cross-correlated our sample with the second ROSAT all-sky survey (2RXS) source catalog (Boller et al. 2016) within a search radius of 30''. This resulted in 1863 matches and amounts to 17% X-ray detection. The distribution of the soft X-ray (0.1–2 KeV) flux of all those NLSy1 galaxies is shown in Figure 13.

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The most important density diagnostic of the NLR in AGNs is the intensity ratio of [S ii]$\lambda 6716/\lambda 6731$ (Osterbrock 1989). There is ambiguity in the literature on the density of [S ii] emission region in NLSy1 vis-a-vis BLSy1 galaxies. Using a sample of Seyfert 1 galaxies including seven NLSy1 galaxies, Rodríguez-Ardila et al. (2000) found that the typical density of the [S ii] emission region in NLSy1 galaxies is lower than BLSy1 galaxies. According to Xu et al. (2007) BLSy1 galaxies avoid low-density (${n}_{e}\lt 140$ cm⁻³) while NLSy1 galaxies prefer low-density but show large dispersion in the density. Recently, Cracco et al. (2016) analyzed the electron density of BLSy1 and NLSy1 galaxies and found no difference in the electron-density distribution between the two classes. Because our sample of NLSy1 and BLSy1 galaxies are much larger than those used in earlier studies, we revisited the electron-density issue of NLR between NLSy1 and BLSy1 galaxies. For this, we estimated the intensity ratio of [S ii]$\lambda 6716/\lambda 6731$ of 2551 NLSy1 and 5533 BLSy1 galaxies. To estimate electron density from this, the python code PyNeb¹¹ developed by Luridiana et al. (2015) was used. Using the PyNeb atomic data "IRAF_09," we calculated electron densities of the NLSy1 and BLSy1 galaxy sample for the intensity ratio of [S ii]$\lambda 6716/\lambda 6731$ between 0.7 and 1.7 with a fixed temperature $T={10}^{4}$ K (see also Cracco et al. 2016). The above criteria provided us density estimates of 2020 NLSy1 and 4744 BLSy1 galaxies.

Figure 14 shows the variation of electron density against FWHM of Hβ for both NLSy1 (dots) and BLSy1 (stars) galaxies. The horizontal dashed line at n_e = 140 cm⁻³ (i.e., $\mathrm{log}{n}_{e}=2.146$ cm⁻³) separates the low- and high-density regions, whereas, the vertical dashed line at 2200 km s⁻¹ separates the sources into BLSy1 and NLSy1 galaxies. Out of the 2020 NLSy1 galaxies, 509 (25%) have $\mathrm{log}{n}_{e}\lt 2.146$ cm⁻³ (zone A), while 1511 (75%) have $\mathrm{log}{n}_{e}\gt 2.146$ (zone B). In the case of BLSy1 galaxies (zone C), 725 out of 4744 objects (15%) have $\mathrm{log}{n}_{e}\lt 2.146$ and the remaining 4018 objects (85%) have $\mathrm{log}{n}_{e}\gt 2.146$ cm⁻³. Our study suggests that about 15% of BLSy1 galaxies in our sample have $\mathrm{log}{n}_{e}\lt 2.146$ cm⁻³, which is not in agreement with Xu et al. (2007) who found BLSy1 galaxies to have $\mathrm{log}{n}_{e}\gt 2.146$ cm⁻³. This disagreement is likely due to the low number statistics of objects used by Xu et al. (2007) in their analysis. However, we find a weak trend of low-density NLR in NLSy1 and a high-density NLR in BLSy1 galaxies. In fact, a very weak but positive correlation between n_e and FWHM(Hβ) is found using the Spearman test of correlation having a correlation coefficient of r = 0.12, and a p-value of $1\times {10}^{-23}$, suggesting lower electron density in the NLR of NLSy1 galaxies than BLSy1 galaxies. The density distributions for NLSy1 (solid) and BLSy1 (dashed) galaxies is shown in the inset of Figure 14. We find mean $\mathrm{log}{n}_{e}$ values of 2.40 ± 0.47 cm⁻³ and 2.54 ± 0.44 cm⁻³ for NLSy1 and BLSy1 galaxies respectively. Applying the K-S statistic, we obtained r = 0.148 and p-value of $7\times {10}^{-28}$ rejecting the null hypothesis that both the distributions are drawn from the same population.

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The mass of the central super massive black hole of our sample of NLSy1 galaxies, as well as the BLSy1 galaxies, were estimated using the virial relation. Considering virial motion of BLR clouds, black hole mass (${M}_{\mathrm{BH}}$) can be written as

$$\begin{eqnarray}&&{M}_{\mathrm{BH}}={{fR}}_{\mathrm{BLR}}{\rm{\Delta }}{v}^{2}/G,\end{eqnarray} \tag{ 6 }$$

where ${\rm{\Delta }}v$ is the FWHM of broad emission line and ${R}_{\mathrm{BLR}}$ is the radius of the BLR (Wandel et al. 1999; Kaspi et al. 2000). The factor f known as scale factor depends strongly on the geometry and kinematics of the BLR (Rakshit et al. 2015). Considering the spherical distribution of clouds, we used $f=3/4$ and estimated ${R}_{\mathrm{BLR}}$ from reverberation mapping scaling relation,

$$\begin{eqnarray}&&\mathrm{log}\left(\displaystyle \frac{{R}_{\mathrm{BLR}}}{\mathrm{lt}-\mathrm{day}}\right)=K\,+\,\alpha \times \mathrm{log}\left(\displaystyle \frac{\lambda {L}_{\lambda }(5100\,{\mathring{\rm{A}}} )}{{10}^{44}}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\right),\end{eqnarray} \tag{ 7 }$$

where K (1.527) and α (0.533) are taken from Bentz et al. (2013) who carefully subtracted the host galaxy contribution to calibrate the relationship between BLR size and the monochromatic luminosity at 5100 Å. The Eddington ratios ${\xi }_{\mathrm{Edd}}$, defined as ${L}_{\mathrm{bol}}/{L}_{\mathrm{Edd}}$ were estimated considering ${L}_{\mathrm{Edd}}=1.3\,\times {10}^{38}{M}_{\mathrm{BH}}$/${M}_{\odot }\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. Following Kaspi et al. (2000), we estimated ${L}_{\mathrm{bol}}$ assuming ${L}_{\mathrm{bol}}=9\times \lambda {L}_{\lambda }(5100\,{\mathring{\rm{A}}} )\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ (see also Xu et al. 2012).

The distribution of black hole mass is plotted in the left panel of Figure 15 for both NLSy1 (solid line) and BLSy1 (dashed line) galaxies. In the case of NLSy1 galaxies, the $\mathrm{log}({M}_{\mathrm{BH}})$ distribution has a mean of 6.9 M_⊙ with a dispersion of 0.41 M_⊙, while in the case of BLSy1 galaxies, the $\mathrm{log}({M}_{\mathrm{BH}})$ distribution has a mean of 8.0 M_⊙ with a dispersion of 0.46 M_⊙. A K-S test applied on the distributions points that both distributions are remarkably different having a K-S statistic value of 0.83 and a p-value of $\lt 1\times {10}^{-150}$. NLSy1 galaxies thus have lower ${M}_{\mathrm{BH}}$ than BLSy1 galaxies. The right panel of Figure 15 shows the distribution of the Eddington ratio. The log $({\xi }_{\mathrm{Edd}})$ distribution for the sample of NLSy1 and BLSy1 galaxies has mean values of −0.34 and −1.03 with standard deviations of 0.34 and 0.42 respectively. This suggests that NLSy1 galaxies have higher Eddington ratios than BLSy1 galaxies. A K-S test confirms the significant difference between the two Eddington ratio distributions with a K-S statistic of 0.64 and a p value $\lt 1\times {10}^{-150}$. Thus, our results are in agreement with those available in the literature that NLSy1 galaxies have lower black hole mass and higher Eddington ratio than BLSy1 galaxies (e.g., Xu et al. 2012).

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To understand the evolution and growth of the black hole it is important to know the connections, if any, between ${M}_{\mathrm{BH}}$ and host galaxy properties. Available observational evidence points to a close correlation between ${M}_{\mathrm{BH}}$ and bulge mass (Kormendy & Richstone 1995; Magorrian et al. 1998) as well as ${M}_{\mathrm{BH}}$ and ${\sigma }_{* }$ (Ferrarese & Merritt 2000; Gebhardt et al. 2000; Kormendy & Ho 2013; McConnell & Ma 2013), which suggests stellar velocity as a fundamental parameter of black hole evolution. Seyfert galaxies are also known to follow the same ${M}_{\mathrm{BH}}\mbox{--}{\sigma }_{* }$ as that shown by the normal galaxy population (Nelson et al. 2004; Woo et al. 2010, 2013). Since NLSy1 galaxies have low-mass black holes, it is crucial to test the extension of the ${M}_{\mathrm{BH}}\mbox{--}{\sigma }_{* }$ relation to the low-mass end of NLSy1 galaxies (Mathur et al. 2001), which is attempted here for our sample. For this, we considered only those sources for which the spectra have a median ${\rm{S}}/{\rm{N}}\gt 10\,{\mathrm{pixel}}^{-1}$, and obtained ${\sigma }_{* }$ for 1789 NLSy1 galaxies. The ${\sigma }_{* }$ is the width (second-order moment) of the best-fitted Gaussian broadening function used in the convolution of our SSP template (see Equation (1)). In Figure 16, the top panel shows the variation of viral black hole mass against ${\sigma }_{* }$. The solid line is the best linear least-squares fit to the data. A moderately strong correlation is found between the two parameters with a Spearman rank correlation coefficient 0.48 and a p-value of $7\times {10}^{-103}$. Using the well-known ${M}_{\mathrm{BH}}\mbox{--}{\sigma }_{* }$ relation for inactive galaxies as defined by Tremaine et al. (2002),

$$\begin{eqnarray}&&\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}\right)=8.13+4.02\times \mathrm{log}\left(\displaystyle \frac{{\sigma }_{* }}{200\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right),\end{eqnarray} \tag{ 8 }$$

we calculated the ${M}_{\mathrm{BH},{\sigma }_{* }}$ using ${\sigma }_{* }$. This relation is indicated by a dashed line in the figure. About 50% of the NLSy1 galaxies of our sample lie below the dashed line and ${M}_{\mathrm{BH}}$ values at the low-mass end have large error bars. This suggests that NLSy1 galaxies do not follow the ${M}_{\mathrm{BH}}\mbox{--}{\sigma }_{* }$ relation of inactive galaxies. This closely follows the finding by ZH06, however, it is in contrast to that of Woo et al. (2015) who report the NLSy1 galaxies follow the ${M}_{\mathrm{BH}}\mbox{--}{\sigma }_{* }$ relation of BLSy1 and inactive galaxies.

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Xiao et al. (2011) presented accurate measurements of ${\sigma }_{* }$ for 76 Seyfert 1 galaxies with low black hole mass using high-resolution spectra obtained from Keck Echellette Spectrograph and Imager and the Magellan Echellette (MagE). Out of these, 22 objects are present in our catalog. However, only for 12 objects, we have a ${\sigma }_{* }$ measurement, non-zero at the 3σ level. The ${\sigma }_{* }$ values of those objects are plotted in Figure 17. The solid line represents the unit ratio line. Note that the spectra of all these 12 objects are obtained by SDSS with a fiber diameter of 3''. The ratio of ${\sigma }_{* }$ between our measurement and that of the Xiao et al. (2011) is 0.80 ± 0.35. The large scatter might be due to low resolution as well as poor S/N in the spectra. However, the figure indicates that our result largely follows the result of Xiao et al. (2011) indicating that SDSS spectra could be used to study ${\sigma }_{* }$ for a large sample. However, to accurately estimate ${\sigma }_{* }$ high-resolution spectra with good S/Ns is needed where detailed modeling of the host galaxy contribution can be carried out.

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Measuring ${\sigma }_{* }$ of high-redshift Seyfert galaxies is very difficult mainly because their cores outshine the host. However, the narrow component of the [O iii] line was used as a surrogate of ${\sigma }_{* }$, though using it various authors reported conflicting results. Most of these studies found that NLSy1 galaxies fall below the relation than the BLSy1 galaxies (Mathur et al. 2001; Botte et al. 2004; Grupe & Mathur 2004). On the contrary, Wang & Lu (2001) and Wandel (2002) found that most of the NLSy1 galaxies fall on the line. The origin of such a conflicting result could be due to the asymmetry in [O iii] line (Véron-Cetty et al. 2001; Cracco et al. 2016) because of which Wang & Lu (2001) used the width of [O iii] line after subtracting the blue wings. A similar argument was also made by Komossa & Xu (2007), who found that the width of the [O iii] line can be used only after subtracting blue wings and excluding the core component of [O iii] lines with strong blueshifts.

To revisit the use of the width of the [O iii] line as a surrogate of ${\sigma }_{* }$, we estimated the width of the narrow component of the [O iii] line (${\mathrm{FWHM}}_{{[{\rm{O}}{\rm{III}}]}_{{\rm{n}}}}$) for all the NLSy1 galaxies, but use only those with a median ${\rm{S}}/{\rm{N}}\gt 10\,{\mathrm{pixel}}^{-1}$ and a narrow component if [O iii] is detected with more than 3σ. We further deconvolved the lines to remove the effect of SDSS spectral resolution and plotted ${M}_{\mathrm{BH}}$ against ${\mathrm{FWHM}}_{{[{\rm{O}}{\rm{III}}]}_{{\rm{n}}}}$ in the upper panel of Figure 18. A correlation is indeed present though weak mainly due to large scatter in the latter. Furthermore, in the lower panel of Figure 18, we plotted ${\sigma }_{* }$ against ${\mathrm{FWHM}}_{{[{\rm{O}}{\rm{III}}]}_{{\rm{n}}}}$. The best linear fit indicated by the solid line, ${\mathrm{FWHM}}_{{[{\rm{O}}{\rm{III}}]}_{{\rm{n}}}}=2.35{\sigma }_{* }$, is superimposed on the dashed line of FWHM = 2.35× standard deviation. There is an indication that many of the objects are falling off the line but large scatter in the width prevents us from making any firm statement. However, the plot clearly indicates that ${\mathrm{FWHM}}_{{[{\rm{O}}{\rm{III}}]}_{{\rm{n}}}}$ can be a proxy of ${\sigma }_{* }$ as previously claimed and widely used in various literature as mentioned above.

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The reasons behind small ${M}_{\mathrm{BH}}$ and large Eddington ratios in NLSy1 galaxies is still unclear. The small Balmer line width that gives rise to small ${M}_{\mathrm{BH}}$ based on the virial relation could be due to geometrical effects. Increasing evidence suggests that NLSy1 galaxies can have ${M}_{\mathrm{BH}}$ and Eddington ratios similar to BLSy1 galaxies. For example, a recent, spectro-polarimetric study of the radio-loud NLSy1 galaxy PKS 2004−447 by Baldi et al. (2016) revealed that the width of the Hα line in the polarized spectrum is 9000 km s⁻¹, which is six times broader than the width seen in direct light, yielding a ${M}_{\mathrm{BH}}$ of $6\times {10}^{8}\,{M}_{\odot }$ and much higher than the $5\times {10}^{6}\,{M}_{\odot }$ estimated using the Hβ line seen in direct light. Also, Calderone et al. (2013), by modeling the optical and UV data for a sample of 23 radio-loud NLSy1 galaxies with a Shakura & Sunyaev disk, found ${M}_{\mathrm{BH}}$ larger than ${10}^{8}\,{M}_{\odot }$, about six times larger than those obtained from single epoch viral black hole mass estimates. Furthermore, Decarli et al. (2008) suggested that if the BLR has a disk-like geometry as opposed to a spherical geometry, the geometrical factor (f) can fully account for the observed mass deficit in NLSy1 galaxies and ${\xi }_{\mathrm{Edd}}$ turns out to be similar to BLSy1 galaxies (see also Liu et al. 2016).

Arguments in favor and against the face-on view of NLSy1 galaxies are available in the literature. Evidences in favor of the face-on view include small widths of the Balmer line due to projection effect (Osterbrock & Pogge 1985; Bian & Zhao 2004), anisotropic emission of Fe ii (Marziani et al. 2001), and detection of γ-rays by Fermi Gamma-ray space telescope in about half a dozen of the radio-loud NLSy1 galaxies (Abdo et al. 2010). Evidence against the face-on view come from the study of polarization observations by Smith et al. (2005). Furthermore, studying a sample of radio-loud NLSy1 galaxies, Komossa et al. (2006) and Yuan et al. (2008) could not confirm the face-on view of NLSy1 galaxies. An estimate of the inclination angle (i) of NLSy1 galaxies can be obtained using

$$\begin{eqnarray}&&f=\displaystyle \frac{{{GM}}_{\mathrm{BH},{\sigma }_{* }}}{{R}_{\mathrm{BLR}}{\mathrm{FWHM}}_{{\rm{H}}\beta }^{2}}={({\sin }^{2}i+{\sin }^{2}\omega )}^{-1}\end{eqnarray} \tag{ 9 }$$

where ω is the half-opening angle of BLR geometry, $\omega =90^\circ$ for a spherical geometry.

Considering a flat BLR ($\omega =0$), we estimated i for all of the objects with $f\gt 1$. Figure 19 shows the distribution of inclination for different ${M}_{\mathrm{BH},{\sigma }_{* }}$. The mean of the distributions are 26°, 46°, and 50° for ${M}_{\mathrm{BH},{\sigma }_{* }}\gt {10}^{7.5}\,{M}_{\odot }$, ${M}_{\mathrm{BH},{\sigma }_{* }}={10}^{6.8-7.5}\,{M}_{\odot }$ and ${M}_{\mathrm{BH},{\sigma }_{* }}\lt {10}^{6.8}\,{M}_{\odot }$, respectively, though all distributions are have  large spreads in inclination. For the purpose of comparison, in the same way, we also calculated i for the BLSy1 galaxies with ${M}_{\mathrm{BH},{\sigma }_{* }}\gt {10}^{7.5}\,{M}_{\odot }$ and similar luminosity like the NLSy1 galaxies. This distribution is plotted with shaded color. The average value in the case of BLSy1 galaxies is $41^\circ$, which is larger than the average inclination of NLSy1 galaxies with ${M}_{\mathrm{BH},{\sigma }_{* }}\gt {10}^{7.5}\,{M}_{\odot }$. This result is consistent with Zhang & Wu (2002) who estimated an inclination angle of about 20 BLSy1 and 50 NLSy1 galaxies and found that the latter have systematically lower inclination angles than the former. Thus, the idea that the narrow width of the emission line in NLSy1 is due to the orientation effect seems to be true.

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